Calories (th)/minute to Horsepower (Electric)

Running at 10 km/h burns about 8,000–12,000 cal(th)/min (8–12 kcal/min) depending on body weight — that's roughly 560–840 W of total metabolic power. Sprinting can hit 25,000 cal/min briefly. But here's the catch: only 20–25% becomes mechanical work; the rest is heat, which is why you get hot. A 70 kg runner at marathon pace (~12 km/h) burns roughly 12,000 cal/min and must dissipate about 700 W of waste heat through sweating.

Before SI standardisation, the calorie was the dominant energy unit in biology because it was defined by water's heat capacity — and most biological calorimetry involved water baths. Measuring oxygen consumption in liters per minute and converting to cal/min via the caloric equivalent of oxygen (4.825 kcal/L O₂) was standard practice. The per-minute rate matched the natural timescale of spirometry measurements. Modern papers have mostly switched to watts, but the older literature is vast.

Metabolic rate scales with body mass to the 0.75 power (Kleiber's law). A 3 g mouse produces about 36 cal/min; a 70 kg human about 1,200 cal/min; a 5,000 kg elephant about 30,000 cal/min. Per kilogram, the mouse is 12× more metabolically active than the elephant. This is why small animals eat constantly and have rapid heartbeats — they burn through their energy reserves much faster relative to their size.

In the late 1800s, Wilbur Atwater burned thousands of food samples in a bomb calorimeter — a sealed steel vessel submerged in water — and measured the temperature rise in cal/min to calculate total energy. He then subtracted energy lost in digestion (measured via feces and urine calorimetry) to derive the "physiological fuel values": 4 cal/g for protein, 4 cal/g for carbohydrate, 9 cal/g for fat. These Atwater factors, over 120 years old, are still the basis for every nutrition label worldwide — remarkably accurate despite their crude origin.

Most wrist-based trackers are 15–30% off for cal/min estimates — some studies found errors up to 93%. They estimate from heart rate, which correlates loosely with metabolic rate but is confounded by temperature, caffeine, stress, and fitness level. Chest-strap heart monitors are better (10–15% error). Gold standard is indirect calorimetry with a face mask measuring O₂ and CO₂, accurate to about 3%. For most people, tracker estimates are directionally useful but not precise.

It's a deliberate rounding for simplicity. The mechanical horsepower is 745.69987... watts — an ugly number for electrical calculations. The electric motor industry rounded to 746 W for clean nameplate ratings and straightforward calculations. The 0.04% difference is far below any motor's manufacturing tolerance. Some standards even use 750 W as an approximation. In practice, the distinction between 745.7 and 746 matters only to standards lawyers and unit conversion pedants.

Divide the hp rating by the motor efficiency and power factor. A 5 hp motor at 90% efficiency draws: 5 × 746 / 0.90 = 4,144 W of electrical power to deliver 3,730 W of shaft power. For three-phase motors, also divide by (√3 × voltage × power factor) to get amperage. Real-world efficiency ranges from 75% for small motors to 96% for large premium-efficiency ones. The nameplate always shows shaft output, not electrical input — a common source of confusion.

Because American homeowners and pool contractors have decades of experience sizing pumps in hp: "a 20,000-gallon pool needs a 1.5 hp pump" is ingrained knowledge. The Department of Energy actually mandated variable-speed pool pumps in 2021 and encouraged watt-based efficiency ratings, but manufacturers still prominently display hp because it drives purchasing decisions. A customer choosing between a 1 hp and 1.5 hp pump understands the difference intuitively; 746 W vs 1,119 W means nothing to them.

NEMA (National Electrical Manufacturers Association) defines standard motor sizes using electric hp: 1/4, 1/3, 1/2, 3/4, 1, 1.5, 2, 3, 5, 7.5, 10, 15, 20, 25, 30, 40, 50, 60, 75, 100 hp and up. These are standardized frame sizes — a 5 hp motor from any manufacturer fits the same mounting bolts. The hp(E) rating is the shaft output; NEMA also specifies efficiency classes (IE1 through IE4) that determine how much electrical power the motor actually consumes.

Not usually. EV manufacturers rate motors in kilowatts because the electrical connection is obvious and kW is internationally understood. A Tesla Model 3 motor is listed as 211 kW, not "283 hp(E)." However, marketing materials often convert to hp for American consumers: "283 horsepower" sounds sportier. Interestingly, EV motors are far more efficient (90–97%) than combustion engines (25–40%), so a 200 hp EV motor consumes far less total energy than a 200 hp gasoline engine.